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Schauder’s fixed point theorem approach for stability analysis of nonlinear fractional difference equations

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  • Sharma, Anshul
  • Mishra, S.N.
  • Shukla, Anurag

Abstract

Analyzing the stability of solutions is a key qualitative aspect of discrete fractional calculus, with many applications. This paper explores a type of discrete equation that incorporates a Hilfer-like fractional difference. We use Picard’s iteration method and Schauder’s fixed point theorem to establish results concerning the existence and uniqueness of solutions. Additionally, we examine both attractive stability and Ulam–Hyers stability for the proposed system. To illustrate our findings, we provide three examples that demonstrate how the main results are verified.

Suggested Citation

  • Sharma, Anshul & Mishra, S.N. & Shukla, Anurag, 2024. "Schauder’s fixed point theorem approach for stability analysis of nonlinear fractional difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s096007792401138x
    DOI: 10.1016/j.chaos.2024.115586
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    References listed on IDEAS

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    1. M. D. Qassim & K. M. Furati & N.-E. Tatar, 2012. "On a Differential Equation Involving Hilfer-Hadamard Fractional Derivative," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-17, June.
    2. Abbas, Saïd & Benchohra, Mouffak & Lazreg, Jamal-Eddine & Zhou, Yong, 2017. "A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 47-71.
    3. M. D. Kassim & N.-E. Tatar, 2013. "Well-Posedness and Stability for a Differential Problem with Hilfer-Hadamard Fractional Derivative," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, December.
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